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Design of polynomial fuzzy observer–controller for nonlinear systems with state delay: sum of squares approach

Author

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  • H. Gassara
  • A. El Hajjaji
  • M. Chaabane

Abstract

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.

Suggested Citation

  • H. Gassara & A. El Hajjaji & M. Chaabane, 2017. "Design of polynomial fuzzy observer–controller for nonlinear systems with state delay: sum of squares approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(9), pages 1954-1965, July.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:9:p:1954-1965
    DOI: 10.1080/00207721.2017.1299813
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